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On the Double Commutator Algebra of QF-3 Algebras

Published online by Cambridge University Press:  22 January 2016

H. Y. Mochizuki
H. Y. Mochizuki*
Affiliation:
University of California, Berkely
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Introduction and Preliminaries. Nakayama [9] suggested that algebras be classified according to the length of a right projective, injective resolution of the algebra as a left module. Tachikawa [10] showed that an algebra is QF-3 (see [12] for definition) if and only if the length is at least one. He [11] also gave some estimations of the length of the resolution besides relating the length to the size of the double commutator algebra of a faithful projective, injective left ideal.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 25 , 1965 , pp. 221 - 230
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1965

References

[1] Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 446–446.Google Scholar
[2] Bourbaki, N., Algèbre. Chap. VIII, “Modules et anneaux semi-simples”, Hermann, Paris, 1958.Google Scholar
[3] Cartan, H. and Eilenberg, S., Homological algebra, Princeton University Press, 1956.Google Scholar
[4] Eckmann, B. and Schopf, A., Uber injecktive Moduln, Archiv der Math. 4 (1953), 75–75.CrossRefGoogle Scholar
[5] Jacobson, K., The structure of rings, Am. Math. Soc, Providence, 1956.Google Scholar
[6] Morita, K., Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku 6 (1958), no. 150, 83–83.Google Scholar
[7] Morita, K., Kawada, Y. and Tachikawa, H., On injective modules, Math. Zeit. 68 (1957), 217–217.Google Scholar
[8] Nagao, H. and Nakayama, T., On the structure of Mo-and Mu-modules, Math. Zeit. 59 (1953), 164–164.CrossRefGoogle Scholar
[9] Nakayama, T., On algebras with complete homology, Abh. Math. Semi. Univ. Hamburg 22 (1958), 300–300.CrossRefGoogle Scholar
[10] Tachikawa, H., A characterization of QF-3 algebras, Proc. Amer. Math. Soc. 13 (1962), 701–701.Google Scholar
[11] Tachikawa, H., On dominant dimensions of QF-3 algebras, Trans. Amer. Math. Soc. 112 (1964), 249–249.Google Scholar
[12] Thrall, R. M., Some generalizations of quasi-Frobenius algebras, Trans. Amer. Math. Soc. 64 (1948), 173–173.Google Scholar